homework 01 – GADHIA, TEJAS – Due: Jan 27 2007, 4:00 am
1
Question 1
part 1 of 1
10 points
A spherical balloon with radius
r
inches has
volume
4
3
πr
3
. Find a function that represents the amount
of air required to inflate the balloon from a
radius of
r
inches to a radius of
r
+ 2 inches.
1.
4
3
πr
3
2.
4
3
π
(
4
r
+
6
r
2
+
8
)
3.
4
3
π
(
r
+
2)
3
4.
4
3
π
(
12
r
+
2
r
2
+
8
)
5.
4
3
π
(
12
r
+
6
r
2
+
8
)
correct
Explanation:
Question 2
part 1 of 1
10 points
An open rectangular box with volume 2
m
3
has a square base. Express the surface area of
the box as a function
S
(
x
) of the length
x
of
a side of the base.
1.
S
(
x
) =
2
x
+
2
x
2.
S
(
x
) =
x
2
+
4
x
2
3.
S
(
x
) =
x
2
+
8
x
correct
4.
S
(
x
) =
x
2
+
4
x
5.
S
(
x
) =
2
x
2
+
2
x
2
6.
S
(
x
) =
x
2
+
8
x
2
Explanation:
Question 3
part 1 of 1
10 points
A newly discovered Jupiterlike planet has
an average radius 11 times that of the Earth
and a mass 314 times that of the Earth.
Calculate the ratio of new planet’s mass
density to the mass density of the Earth.
Correct answer: 0
.
235913 (tolerance
±
1 %).
Explanation:
Let :
R
np
= 11
R
E
and
M
np
= 314
M
E
.
The volume of a sphere of radius
R
is
V
=
4
3
π R
3
. The (average) density
ρ
of a body is
the ratio of the body’s mass to its volume,
ρ
=
M/V
. Planets are spherical, so the (average)
density of a planet of a given mass
M
and a
given radius
R
is
ρ
=
M
4
3
π R
3
.
Comparing the newly discovered planet to the
Earth, we have
ρ
np
ρ
E
=
parenleftBigg
M
np
4
3
π R
3
np
parenrightBigg
slashbigg
parenleftBigg
M
E
4
3
π R
3
E
parenrightBigg
=
parenleftbigg
M
np
M
E
parenrightbiggslashbiggparenleftbigg
R
np
R
E
parenrightbigg
3
=
314
(11)
3
=
0
.
235913
.
Question 4
part 1 of 1
10 points
The number
x
= 0
.
0416 has how many
significant digits?
Correct answer: 3
(tolerance
±
1 %).
Explanation:
Figures except zeros to the left of the first
nonzero digit are all of significance.
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homework 01 – GADHIA, TEJAS – Due: Jan 27 2007, 4:00 am
2
Question 5
part 1 of 2
10 points
A person travels by car from one city to
another. She drives for 21
.
1 min at 81
.
8 km
/
h,
14
.
1 min at 86
.
4 km
/
h, 49 min at 36 km
/
h,
and spends 13
.
5 min along the way eating
lunch and buying gas.
Determine the distance between the cities
along this route.
Correct answer: 78
.
4703
km (tolerance
±
1
%).
Explanation:
Distances traveled are
x
1
=
v
1
t
1
x
2
=
v
2
t
2
x
3
=
v
3
t
3
Then the total distance traveled is
x
=
x
1
+
x
2
+
x
3
= (28
.
7663 km) + (20
.
304 km) + (29
.
4 km)
= 78
.
4703 km
.
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 Spring '08
 Turner
 Acceleration, Work, Velocity, Correct Answer, m/s, Transverse wave

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